What Dostoyevsky could not forsee in the relation of mathematical reason to capriciousness is that one day science would avail itself of its apparent stolid regimentation. That is what quantum physics revels in: the discovery of randomness as the essence of the physical world; that what we can never measure because of Heisenberg, because of Einstein-Podolsky-Rosen: that is what gives true awe to what we sense. Modern physics is not an attempt to explain that randomness -- that quantum flux -- but only attempts to catalog it; not, as it were, to understand its literal truth, but rather to marvel at its creative fury.
Every new quantum equation serves to add a new brushstroke to the oeuvre, to approach with dazzling color an asymptote of comprehension and predictability; and not out of pure aesthetics, to be sure, or even any secular faith, but rather out of satisfaction at the non-rigidity of it all. So science and art can converge not because they are similar, but because the creativity of mankind spurs them both on similar paths, paths which meet at the heart of the human desire to have a chaotic peace of mind.